3-D and 2-D Permutohedrons in Nature


Fig. 1
(A and B) Complementary [G3NO3]2+ (yellow) and HSPB6–(green) tiles, with their corresponding edge lengths, defined by the distance spanned by neighboring guanidinium and sulfonate ions, respectively. (C) Schematic representation of an unfolded q-TO based on the complementary [G3NO3]2+(yellow) and HSPB6– (green) tiles, illustrating the edge-shared N-H···O-S hydrogen bonds. (D) The q-TO. The open squares in (C) and (D) correspond to the openings on the surface of the q-TO that enable the formation of channels between adjacent q-TOs in the solid state.

From “Supramolecular Archimedean Cages Assembled with 72 Hydrogen Bonds” by Yuzhou Liu, Chunhua Hu, Angiolina Comotti, and Michael D. Ward, Science, 22 Jul 2011, Vol. 333, Issue 6041, pp. 436-440.

Fig. 2 A vortex field on Saturn

This entry was posted in Math and tagged , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s